# A series of posts on a few series of tweets (by me) on (my research on foundations of) QM—1

0. Initial remarks:

OK. It’s been a little while since I wrote my last post here.

Actually, it so happened that for a while after my last post I didn’t find anything well suited for writing a blog-post. I was also busy studying topics from Data Science. It’s true that during this time I did make a few comments at others’ blogs, but these were pretty context-specific. I couldn’t easily think of making a (more general-purpose) post out of them.

At the same time, some of the things that I read on QM—whether in pop-sci books or at others’ blogs—did prompt me to note a few comments. These were very brief points. They were better fitting only as tweets—as side-remarks made in the passing. So, I tweeted them. My twitter page is here [^].

… I now realize that quite a few of such tweets (on QM) have got accumulated. So it’s high time that these occasional notings got moved here too, together with some explanation to go with them. That’s precisely what I am going to do now, in this series of posts.

Most of these points (from the tweets) refer to my Outline document on QM which was posted at iMechanica about 6 months ago [^]. The tweets wouldn’t make any sense to someone if he hasn’t thoroughly gone through this document first. So, I do assume this context here.

In fact, most of these tweets are rather direct implications of what I had already noted in the Outline document. These points (from the tweets) were quite clear to me even back then, when I wrote the document.

However, while writing that document, my purpose was, first and foremost, to state the most salient building blocks and points of the theory and to focus on the overall way in which they connect together. Thus, what I wanted to give, via that document, was a definitive sense of the overall framework—hopefully in a logically complete manner. I was in fact worried a bit that some parts of these complex considerations might get slipped out of my mind once again as they had done in the past (before I wrote that document!) [In retrospect, I think that on this count, I did a pretty good job in the Outline document. I haven’t been able to think of a really essential part of the framework which I had in mind and which inadvertently got left out from it.]

Another reason I didn’t go into detailed implications right in that document was this: I also thought that anyone who knows the mainstream QM well, and also “gets” the logic given in my document well, would be able to very easily reach these further inferences completely on his own—for instance, my position on the wave-particle duality. So, I didn’t separately mention such points in that document even if I knew that points like these would be of  much greater interest to the layman. The Outline, although very simple it looks, was definitely not written for the layman. (I tried to keep it as simple in exposition as possible, in part because I didn’t care to be seen as a respectable physicist anyway. All that I was concerned about was QM, and the new conceptual framework.)

So, all in all, it’s not an accident that I should be touching on many points like the wave-particle duality only later on, first via tweets! These really are only implications / consequences.

Anyway, here in this series we now go with these tweets of mine (made over the past month). While reproducing them here, I have expanded the short-forms or abbreviations, and also have added few additional bits of content too, just to get more streamlined sentences. Each tweet is then followed by some explanation, which very rapidly became very long—long enough that I couldn’t possibly compress all the QM-related material (tweets and my explanations of them) into a single post. So, I have no choice but to make a series of them!

1. Schemes for nonlinear QM proposed by others:

I tweeted on 12 July 2019 to this effect:

“Schrödinger eqn. revisited” by Schleich et al.  [(.PDF) ^] . Yes, it presents a nonlinearity. But no, it doesn’t even consider the physical fact that all the potentials in reality come about only from superpositions of the singular potentials of individual electrons and protons. See my Outline document.”

Indeed, what I said here applies to each and every nonlinearity-based argument (except for mine!) which has ever been offered by way of attempting a resolution to the riddles of QM—in particular, the measurement problem.

To quote from Ian Stewart’s book: “Does God Play Dice? (2/e)”, several people have proposed nonlinear theories, including:

“L. Diosi, N. Gisin, G. C. Ghirardi, R. Grassi, P. Pearle, A. Rimini, and I. Percival.”

I had very briefly gone through some of these proposals. Actually, I had mostly got to know about their proposals by reading descriptions and remarks on them as made by other commentators. However, at times, I also went rapidly browsing through some of their arXiv papers. I had come to the conclusion that what they were putting forth wasn’t anything like my ideas (later mentioned in the Outline document). To quote Stewart here,

“In all of these theories the interaction of a quantum system with its environment produces an irreversible change that turns the quantum state into an eigenstate. However, all of these theories are probabilistic: the initial quantum state undergoes a kind of random diffusion which ultimately leads to an eigenstate.” (ibid.)

To be honest, I am not sure whether all these proposals could be characterized as involving random diffusion or not. I don’t know these theories to the required level of detail to be able to confirm or deny Stewart’s characterization. However, there certainly is this element of an initial quantum state getting collapsed precisely to the measured eigenstate, which appears in all of them—and I don’t accept that idea in the first place (as explicitly put forth in my Outline document).

In a slightly different context, Stewart also notes:

“There is some interest among physicists in what they call `quantum chaos’, but quantum chaos is about the relation between non-chaotic quantum systems and chaotic classical approximations—not chaos as a mechanism for quantum indeterminacy.” (ibid.)

OK, this is one conclusion which I very distinctly remember I had reached on my own too. I guess this was in November 2018, when I had googled on “quantum chaos.” Subsequently, I re-checked the matter again (just to be sure) in February ’19 (i.e., just days after posting my Outline document.)

I agree that Stewart’s characterization is right on the target here. IMHO, you don’t need to take recourse to the prior studies of “quantam chaos” very seriously if either the QM foundations or the very feasibility of the quantum computer are your concerns.

2. A bit on my PhD-time research:

I made a series of 4 tweets on 18 July 2019. The first two of these dealt with my old, PhD time approach to photon propagation. Let me note here a clarification regarding what all other work I had performed during my PhD, before coming to my old (PhD-time) approach to QM (which I will address in the next section).

The first thing to note is that my work on QM had formed only a part (may be about 1/4th part or so) of whatever studies and research I had done during my PhD.

The other parts of my PhD thesis were notably related to the studies of the classical second-order partial-differential equations, and their computational modeling using stochastic processes. The equations on which I thus focused my attention were: the Helmholtz equation, the diffusion equation, and the Poisson-Laplace equation. In addition, I had also picked up a study of elasticity, and had added a conjecture about the possible applicability of some random-walks type of processes for modeling the classical tensor fields (of stresses and strains as used in engineering). Let me go over all these topics in brief.

2.1 Work on the diffusion equation:

I think I have posted many entries at this blog about my work on diffusion equation. So let me not regress into it all once again. Let me just note that I basically showed that, contrary to what post-graduate texts in maths (published by AMS) say, the diffusion equation does not necessarily imply an instantaneous action at a distance (IAD).

The IAD in diffusion, I pointed out, was an outcome of the features of the solution theory (Fourier’s theory, and also of Einstein’s analysis of the Brownian movement). But IAD was not necessarily implied either by the local physics of diffusion phenomena, or by the partial differential equation that is the diffusion equation. [Here, remember, a differential equation always, invariably, necessarily, etc., is local in nature—it refers to an infinitesimal CV (control volume) or CM (control mass).]

In particular, I pointed out that the compactness of the support of the solution was the crucial issue here—whether the support was infinite (as in Fourier theory and in 2nd half of Einstein’s c. 1905 paper), or finite (as in any subdomain-based numerical method, or in the Brownian movement, i.e., the first half of the same paper by Einstein). In my view of the things, you can always transition from a collection of finite subdomains to an infinity of infinitesimal CVs that are still distributed over only a finite interval, via a suitable limiting process. The finite support, of course, could grow in extent with time.

These observations had never been made in about 200 years of the existence of Fourier’s theory. (Go ahead, hunt for the precedents!) You have to make this distinction between a (local) PDE and its (possibly global) solutions obtained after conducting integration operations, and in this entire process, you have to be careful about not elevating a mere ansatz or an integration method to the high pedestal of “the” (provably unique) solution. That’s in effect what I had argued.

2.2 Work on the diffraction phenomenon (Huygens-Fresnel theory):

I also had a neat (though smallish) result concerning the obliquity factor in diffraction. I went through Huygens’, Fresnel’s and Kirchhoff’s analyses of the diffraction phenomenon (involving the Helmholtz equation—i.e., the spatial part of the wave PDE), and then pointed out the reasons why the obliquity factor could not be regarded an essential characteristic of the diffraction phenomenon itself.

Once again, the obliquity factor turned out to be a feature of how the analysis—specifically, the integration operations—had been set up. It was a feature of the mathematical solution procedure adopted for this problem. In diffraction, there was no fundamental physical process which operated in an anisotropic way, compelling the wavefield to have a greater amplitude in the forward direction and zero in the backward direction.

However, explanations for some 187 years (since Fresnel’s work) had characterized diffraction as an inherently anisotropic phenomenon. Yes, right up to my old copy of Resnick & Halliday. There was a surprise in it for me because while Fresnel was just a railroad engineer who had taught himself maths, Kirchhoff surely was a master of PDEs and their integration techniques. But this fact still had escaped even Kirchhoff.

I pointed out how even if you do keep isotropy to the Huygens’ wavelets, given the geometry of the interaction of Huygens’ wavelets and the surfaces where BCs are applied, you would still end up with the same amplitudes as those obtained by Fresnel’s or Kirchhoff’s analyses.

Come to think of it, you could even pick up this line of argument and apply it to any analysis that seeks to derive an expression for a field inside a finite domain by appeal to a pair of forward- and backward-going processes occurring within that domain; e.g., an analysis involving the advanced and retarded waves, or the transactional waves in certain interpretations of QM, etc. You just have to be careful about what BCs and integrals are being set up and how the integration processes are being conducted, that’s all!

2.3 Computational modeling of transient heat conduction:

I then tried to apply the random walks-based approach (RW) to model transients in the heat conduction, as they occur in a moving boundary problem, viz. the melting snowman. Since my focus was on conduction, I grossly simplified all the other aspects of this problem. (Having just come out of an illness, I would get easily tired back then.) The problem I considered was that of melting of a snowman.

Consider a snowman in the form of a vertical right-circular cylinder which is placed on a relatively large block of ice below. The snowman absorbs heat from the atmosphere by radiation and convection at its external surfaces. The absorbed thermal energy then flows through the volume of the cylinder to the relatively large block of ice underneath (which was regarded as infinitely large in the simulations). The temperature gradients of course come to exist. The heat in the atmosphere brings the external surface to the melting point of ice even as the interior portions remain below it. So, the surface melts—phase-transition ensures a constancy of temperature at the surface. The melting is more pronounced at the sharp corners. The resulting water gradually slips down, forming a thin and continuous layer on the external surface. (I ignored the fluid flow in my simulation.) All in all, the sharp cylindrical snowman slowly acquires a thumb-like shape over a period of time, and then still continues to shrink down in size.

I first tried to apply RW for heat conduction in this scenario, but soon found that there was a great deal of noise due to randomness. So, I set up a “conversion” from the particles-based approach of RWs to a local, continuum-based approach, thus ending up with a description which was essentially equivalent to a cellular automata-based one. I then performed the simulations with this CA-based approach (in 3D), compared the changing external contours of the melting snowman with an actual experiment (done at home, for less than Rs. 200/- as the total cost—for thermocouple wires, basically), and presented a paper at an international conference.

This piece of work added the necessary component of “engineering” and “experimentation” to my thesis. While my guide was always happy with my progress, he also was a bit worried that examiners might look at my thesis and conclude that it was all a useless piece of theoretical, almost scientific work—it had little “practical” component to it, and so, couldn’t qualify for a degree in engineering. So, he was quite relieved when I discussed this idea of snowman with him—he immediately gave me a go ahead!

2.4 Conjecture for using RWs for modeling tensor fields:

Then, in addition, I also had this conjecture regarding the feasibility of random walks for simulating tensor fields. Since I haven’t spoken at length about it here at this blog, let me note something here.

There were certain rigorous mathematical arguments (coming from Ivy League professors of mechanics as well as from seemingly competent but obscure Russian authors) which had purportedly shown that stochastic processes like random walks could provably not be used for simulating the stress/strain fields.

Yet, I was confident of my conjecture, out of some basic considerations which I had in mind. So I gave a conference presentation on it (in an international conference on mathematics), and also included it in my thesis.

Much later on (after my PhD defence), I grew further confident that this conjecture should definitely come to hold; that it could be proved. That is to say, the earlier (intricate) proofs by reputed mechanicians / mathematicians could be shown to have holes in them. (Not that my argument was flawless either. A professor had spotted a weak link in my argument at that conference, and had brought it to my attention in a most gentle, indirect manner.)

Then, some time still later on, I ran into some “simple” but directly useful work by a young Chinese author (perhaps a PhD student). If I remember it right, he had published this paper while working in China itself. His work was similar to an intermediate step I had in mind, but it was much more complete, even neat. No, he was not concerned with the random walks as such. All that he did was to give a working model for constructing stress/strain fields, by starting with a finite 3D unit cell having an internal structure of a truss and treating it as if it were a finite approximation for an infinitesimal CV of the continuum. I had somewhat similar ideas, and had in fact inserted a couple of screen-shots of the truss-based simulations I had conducted for a preliminary study. But he had gone much further. If I recall his paper right, he had even arrived at the right values for the truss-related parameters (like stiffnesses of the members) if this unit cell was to converge to the continuum equations of elasticity in the limit of vanishing size.

Now, by regarding the process of re-distribution of forces along the truss members as an abstract flow, and by randomizing it (discretizing it in the process), it should be easily possible to come to a proof of my conjecture. Also a neat computational simulation. Of course, the issue is not as simple as it looks on the surface. Free surfaces in a multiply-connected domain pose a tricky issue—they deform freely, and so, uniqueness becomes tricky to handle. Even then, with sufficient care (or appeal to ideas from CoV) I am sure that it can be done.

OK. I will do it some other time in future! (This has been a TBD paper on my list for almost a decade or so by now; I simply don’t run into suitable ME/MTech students for me to guide on this topic! … Anyway, this blog is in copyright, just in case you didn’t notice it…)

3. My PhD-time work on QM (photon propagation):

Alright, finally we come to my PhD-time work on photons propagation. In a series of tweets, I said (on 18 July 2019):

“1/4. My old (PhD-time) approach, then called “new approach” and also as FAQ (Fields As Quanta): I’ve abandoned it; the one in the Outline document replaces it completely. FAQ anyway dealt with only the propagation of only the photons, not their generation or absorption (i.e. it didn’t deal with the creation/annihilation operators). FAQ didn’t deal with the propagation of other particles, viz., electrons, protons, or neutrons either.”

and

“2/4. FAQ still remains valid as an abstract description, as referring to the propagation characteristics of photons in the limit that the medium is continuous (i.e., it is homogenized from discrete and dispersed atomic nuclei), i.e., if the propagation dynamics is diffusive, not ballistic.”

About this second tweet, I subsequently had second thoughts soon after, and so I noted, right on the next day (on 19 July 2019) the following comment (a reply) to it:

“Umm… I am not sure precisely what all considerations should enter into taking the limits (for arriving at the propagation characteristics of photons as conceptualized in my older, PhD-time, approach). Would have to work through how the Schrodinger formalism (and hence my new approach) goes from $\Psi$ and photons to the classical, dynamical EM fields. To be done in future. But yes, FAQ dynamics *was* diffusive, that’s for certain.”

Thus, I first said that FAQ still remains valid, when seen as an abstract description. However, just one day later, I also pointed out the more basic and possibly tricky issues there might be—viz., finding the right kind of limiting processes which start from the Schrodinger formalism and end up at Maxwell’s equations.

I feel confident that people must have thrashed out this topic (TDSE $\Rightarrow$ EM) long time ago. It’s just that I myself have never studied the topic so far (in fact I haven’t even done the literature search on it), and so, I don’t have a good idea about what all technical issues might get involved in it.

Thus, I will have to first study this topic (from the mainstream QM to EM). Only then would I be able to understand the mapping well enough that I could understand the Hertzian waves right in the QM settings. It’s only after this stage that I will be I be able to say something definitively about the manner in which FAQ can really hold, and if yes, how well. Worrying about the right kind of a limiting procedure would be just a part of it, but an important one. … So yes, you can take these particular tweets with a pinch of salt.

4. How did I get to my old PhD-time approach for photons (i.e. FAQ), in the first place?

OK. Now that we are at it, here is a question that might have arisen in your mind: If I didn’t know QM well back then (during my PhD-studies days), then how could I dare propose this approach (viz. FAQ) so confidently?

Ummm… Let’s leave the daring and the confidence parts aside for now. Let’s focus on the “how” of it—how I got to my ideas. This part is much more interesting. At least to me.

How precisely did I end up at the idea of FAQ?

Well, I began with a kind of a “correspondence principle” (not in the Copenhagen sense of the term; read on). Briefly, the “correspondence” which I had in mind was the fact that single photons one-at-a-time mark only isolated dots on the CCD surface, but in the large-flux situations, their density pattern converges to the continuum interference pattern as described by Young.

So, I imagined a point-source emitting photons. Mind you, photons for me were, back then, spatially discrete particles of light, a la Einstein and Feynman—both their ideas had held a tremendous sway over my thinking back then.

I then imagined an ideal absorber in the form of a spherical surface kept at some distance from the source, somewhat like your usual Gaussian surface from electrostatics, but the difference here was that while the Gaussian surface is imaginary and allows anything to move through it freely, here, it was an actual absorber, albeit imaginary. This spherical surface was centered on the same point source. I asked myself what kind of variations in density should light show, in the continuum description, on this concentric spherical surface if its radius was varied a bit. In essence, I was developing my logic by starting from Gauss’ theorem and the Poisson-Laplace equation.

I then transitioned, in my ideas, to the Helmholtz equation by imagining a time-steady waviness to the field. Now, if the radius of the sphere were constrained to be an integral multiple of the spatial period (i.e. wavelength) of light, then the total quantity of photons being absorbed at the spherical surface should remain the same for a sphere of any such a radius. The only rationale which could justify this assumption was: to have a conservation principle in place, by asserting that photons are conserved while they still are in transit through the empty space (i.e. before they get absorbed on the spherical surface). Again, remember, I was using the idea of photons as if they were spatially discrete particles, like the grains of mustard seed.

Conservation principles are neat, I had learnt mostly in reference to the ample evidence I found in engineering sciences. (Even if I were to know about Noether’s theorem, I would have disregarded it—such was, and still is, my temperament. I think that this theorem is merely a reformulation of a very narrow range of physics—one that is restricted to merely 2nd-order linear PDEs. Anyway, read on…)

If the photon number conservation was to be had in theory (during propagation) at integral multiples of $\lambda$ for the radius of the sphere, then was there any sound reason to give up conservation when the radius was $(n+1/2)\lambda$? (Here I am assuming that at zero radius, the light has the maximum amplitude.) Couldn’t we explain the complete darkness at these odd radii by positing that the photon was still there—it’s just that the sphere of that particular radius didn’t absorb it? After all, we could always posit a variable called the absorption fraction which would be related to the local amplitude of the spatial wave, right? That’s how I decided to conserve the photon number, and thereby, shift the burden of the variable levels of brightness at the absorber by appeal to a photon-absorption process that varied in efficiency precisely in response to the local wave amplitude associated with the tiny grain which was photon. (I regarded this grain as a localized condition in the luminiferous aether.)

Now, the next question was: If the photons had a ballistic dynamics (i.e. a straight-line motion), then the point on the spherical surface where a given photon eventually would land, would have already been determined right at the source point—some internal processes in the emitter material would be responsible for ejecting it at random orientations, which would also determine its landing location. (Dear Bohmians, do you see something familiar? However, please note, this was entirely my own thinking. I had not come across Bohm back then. Please read on.)

I thought that while this was possible, it was also possible that the photons could also undergo random-walks. How did I introduce random walks?

Well, the direct experimental evidence showed that this propagation problem had two essential features: (i) many discrete spots which go in a limit to a continuous pattern of finite densities, and (ii) random locations on the absorber surface where the grainy photons land, i.e., no correlation between the two points where any two successive photons get absorbed.

Since the continuum viewpoint of light (Young’s waves) had to be reached in the limit, it was important to keep in mind always. It was here that I happened to recall Huygens’ principle. I was also quite at home with the idea of randomly intersecting a 3D surface with a linear probe—I had already studied stereology at the University of Alabama at Birmingham (UAB).

Huygens’ principle involved every point of space as if it were some kind of a “source” for the new (Huygens’) wavelets. The Young pattern could be obtained by superposing all the Huygens’ wavelets. The discrete spots could be had by dividing the surface of the Huygens wavelets and taking the individual surface patches to vanishing size (a la mesh refinement). This satisfactorily addressed the first essential feature noted above (viz. discrete spots). As to the second feature (randomness) it could also be satisfied by randomizing the selection of the spherical patch on the Huygens’ wavelet (a la stereology).

This much part, I in fact had already completed when I was right at UAB, completely on my own, though I had never shared this idea with anyone. I guess it was already over before 1992 came to an end.

More than a decade later, now in Pune: Starting with Gauss’ theorem, and touching on the Huygens process and stereology, and now, also throwing in the vector addition rules for ensuring that right phases appear throughout the propagation, and so, local amplitudes also come out right in the large-flux situation, I could get to my diffusive dynamics for the spatially discrete photons.

I did suspect that this procedure (of randomizing the selection of a point on any of Huygens’ wavelets) meant that the photons would have to be imagined either as (i) getting scattered everywhere during their propagation, or (ii) possibly getting annihilated after travelling even just an infinitesimal distance in empty space, and then, somehow, also getting re-created  (the time lag between the annihilation and the subsequent creation being zero), effectively satisfying the conservation principle. On either count, the photon would keep changing its directions randomly, because the point on the surface of the Huygens wavelet was randomized.

Of course, I could not figure out a good physical reason for such a process.

Scattering of one photon by other photons seemed implausible—though I couldn’t figure out any particular reason why it would be implausible. Anyway reliance on scattering led to an impossible situation when there was only one photon inside the interference chamber.

There also was no proper physicist who would even so much as be willing to just listen to me. (I tried more than 15–20.) On the other hand, so many leading ones among them were offering descriptions of QM in terms of a random “quantum foam/froth” which produces and annihilates any particles anywhere anytime—even massive ones and even in empty space at any random time. So, I thought that my idea of continuous disappearance and appearance but in a different direction, would not be found too odd.

(Discussions of foundations of QM has improved by leaps and bounds since engineers started taking interest in building QC. In fact, recently, a somewhat similar remark also came from Dr. Sabine Hossenfelder on her blog. But I am talking of those days—around 2005 times.)

Of course, since I myself didn’t have even an iota of a physical understanding regarding such virtual annihilation/creation pairs for photons, but since they were necessary in my scheme because I had randomized not the source point but the Huygens surface, rather than going full wacko (as most any physicist in my situation would), I did what any graduate student of engineering would do: I simply refrained from mentioning any such implications for a possible physics of it, and instead chose to phrase my description of the process in terms which heavily relied on the well-established, well-reputed, classical principle of Huygens’.

No one ever asked any questions on this part either. Neither in conference, nor in PhD defence, nor even after sharing my papers with physicists (some of who had on their own requested my papers). So, it kindaa went through!

Phewww…. All the hoops that a hapless PhD student has to jump through, just to get to his degree! (In my case, it was even worse: these were the closed surfaces of the Huygens wavelets, not mere closed curves as in the hoops.)

So, that’s how I had arrived at my PhD time approach. I did it by randomizing the spherical surfaces employed in the Huygens’ process, and by imagining a spatially discrete particle of the photon at all such locations at each one of the subsequent instants. The movement of the photon, when it goes on cutting the respective surfaces of all the freshly generated series of Huygens’ wavelets, when the cutting is randomized, obviously forms a simplest kind of a Weiner process—it’s the direct counterpart of the random-walks, but for wave-fields.

People right from Ulam et al. had proposed and used random walks (aka Monte Carlo) for diffusive and potential fields, for 50+ years. However, none had added just some more calculations with the wave- and displacement-vectors to account for the phases, and thereby generalized the random-walks to be able to handle the wavefields too. That was another neat thing to know. (Yes, please, do go ahead! Do hunt for the precedents!!)

Anyway, that’s how the FAQ dynamics came to be diffusive.

And all said and done, it did come to reproduce a seemingly same kind of a transition from a pattern of random dots to the Young interference pattern as experiments had shown!

One final point. But why did I disregard the ballistic dynamics—which would have all randomness concentrated only in the source and let photons fly straight? Yes, come to think of it, if you do assume a spatially discrete nature for the photon, then there is obviously no good reason to deny such a possibility.

Here, I am not sure, because I don’t remember having writing down any note on it. So it’s kindaa hard to tell now, from a distance of years. I will try to reconstruct some possible considerations starting from some indirect points, and purely from memory.

I seem to recall that I was apprehensive that what I called “size effects” might come into picture and make this approach unsound. I mean to say, a perfectly uniform randomness (distributed over the entire emitter surface) was hard to imagine as the emitter surface became ever smaller, and reached the natural limit of a single atom. For one thing, the emitted quantity might get affected, I thought. Secondly, single atoms, acting as emitters, had to have some directionality to their emissions because their orbitals [whatever it meant—I didn’t have a good idea about them back then] weren’t always spherically symmetric. I think I had considered this point.

Did I consider the delayed-choice kind of considerations? I think I did, but in some simple indirect ways, not very carefully or systematically. I mean to say, I don’t remember going through write-ups on the delayed-choice experiments at all, and then taking any decision. I rather remember thinking in terms like a camera shutter suddenly coming in the way of a photon when it’s still in mid-flight and all. If the shutter were to be a perfect sink (one that didn’t re-emit the photon), or if it were to re-emit photons from a different location on the shutter surface (after internal energy undergoing some unpredictable oscillations within the shutter material), then it would adversely affect the final pattern on the screen, I had thought. The real-time changes for the propagating photon might get better handled by distributing randomness over the entire spatial region of the chamber, I had thought.

But I think that all in all, it wasn’t any such careful consideration. I chose the randomized Huygens’ process because I thought it gave good enough an explanation.

In the final analysis, there are too many problems with this entire approach—even with just a spatially discrete photon anyway, and furthermore if it comes embedded in a description that has no IAD anywhere in itself. Some or the other part of QM will then have to keep getting violated. You just can’t avoid it. So, the best way to understand QM is not to begin with photons but with electrons—and with the Schrodinger formalism. The measurement problem is the only remaining issue then.

5. Homework for the skeptics among you:

Go through my PhD abstract posted at iMechanica even before the defence [(.PDF) ^], and check out if what I wrote above, purely on the fly and purely from memory, matches with what I had officially reported back then, or not. If you find serious discrepancies, please bring them to my notice. Thanks in advance.

Of course, now that I’ve completely abandoned the grainy description of photons as the actual physical reality, all the above doesn’t much matter. FAQ, even if valid, would have to be taken as only a higher-level, abstract description of an entirely different kind of a mechanism.

So, let’s leave this entire PhD-time approach right behind us (forever), and continue with the next tweet in this series. They directly deal with the aspects of my latest approach (as in the Outline document)… However, I will pick it up in the next post. It’s almost 5900 words already! Give me a break of at least a 10–15 days. Until then, take care and goodbye.

A song I like:

(Marathi) “ambaraatalyaa niLyaa ghanaachee”
Singer: Ramdas Kamat
Music and Lyrics: Veena Chitako

# How I am simultaneously both: right, and probably, partly wrong…

[A few inline updates added, and some very minor copy-editing done at a few places, on 2014.12.28.]

In my research, I have found that I am simultaneously both right and, probably, partly wrong.

* * * * *   * * * * *   * * * * *

First, the probably partly wrong part. I will assume as if I am actually (partly) wrong, and write it. (The probability that I am wrong is very high.)

The error concerns my theory for the mechanism of propagation of photons that I had put forth almost a decade ago, formally published in Dec. 2005. I had had that idea since 1991/1992. The more recent experimental evidence, I guess, shows it wrong.

First, on to the mistake, and then, to the experimental evidence. [Here, I will not bother explaining myself. Instead, I will assume that you are well familiar with my published papers, know about the field, and thus, go straight-away to the heart of the matter.]

Ok. About the mistake. Essentially, it is that the mechanism that I had proposed implied that photons in free space have a diffusive dynamics. My browsing of the experimental evidence indicates that they instead have a ballistic dynamics. The theory, as presented in the papers, therefore, fails.

The experimental evidence comes from the PDC entangled photon pairs—i.e., if I get the evidence right.

Consider two PDC entangled photons. They are found at the intersection of the two cones. Assume that in experiment, the cones can be intercepted by detectors lying in a plane normal to the central axis, at any arbitrary distance. Suppose that the detectors’ plane lies at distance $x_1$ from the crystal and that you detect the entangled pair “simultaneously” at a certain time $t_1$. The question is, if the detectors’ plane is placed at a distance $10 x_1$, what would be the detection time? If $10 t_1$, then it obviously means that the dynamics is ballistic.

I presume that this in fact is the case in the actual experimentation, even though I could not easily find any direct experimental data to verify the same. But there is another reason why the dynamics must be ballistic.

If the dynamics were to be diffusive, then the probability of the simultaneously generated photon pairs ending up on the intersection spots would be so small that no one would think of producing photon pairs this way.

In my theory, the dynamics is diffusive because the photons change their directions randomly. This circumstance is impossible to realize in free space, because photons wouldn’t collide. By Pauli’s principle, two electrons would, but not two photons. Photons being bosons can occupy the same region of space without noticing each other.

[Update on 2014.12.28: The mistake isn’t “elementary.” Take two identical billiard balls and let them undergo perfectly elastic collision. The outcome is, in a way, the same as if two balls were to pass through each other without noticing the other’s presence. Think a bit more about this example and the mathematical (or “statistical”) in-distinguishability. … And also realize, despite Pauli’s principle, the mainstream QM doesn’t have anything to say on the matter: they don’t localize the photon while it is in propagation, in the first place. So, it’s not as if the issue has already been clarified by the physicists in their text-books and that the engineer is being audacious. BTW, most of the physicists who at all replied my emails, including an “Objectivist” one, had advised me to first study physics well, presumably before writing papers.]

I myself detected the error; none else pointed out. Indeed, none else (say a student or a reviewer) even hinted at a possibility. Not a single physicist to whom I had on my own sent my paper, came up with this objection.

The only person(s) to raise any sort of objection here were, hold your breath, my thesis examiners! They had begun by asking me whether the simulation I performed was for electrons or photons. There had followed a string of questions on their part, and simple, examinee-like assertions (rather than logically most thoroughly sound answers) on my part. They had kept the matter in abeyance before moving on to the next set of questions.

Yes, IMO, they could have granted me a PhD.

The reason is, firstly, that I had worked very hard on it and therefore had ample other material to justify a PhD. (One of the examiners had noted the relatively unusually large volume of work submitted for the degree.) I had other work or observations or results concerning numerical modelling, Huygens-Fresnel principle, and diffusion equation, and some of it still looks very fresh and original to me even now (especially the last; more on it later, right in this post).

Secondly, even for wave-fields, the description I presented could still be used as an abstract model for simulation of other linear wave fields (and I had pointed out some of these applications right in my papers), though, now, not for photons in free space.

Thirdly, many of the non-mainstream assumptions which I explicitly made do not get invalidated by the current experimental evidence, and remain worth taking note of. These include identification of photon (i) as a spatially localized phenomenon or condition  (ii) in aether. To build a new theory is the whole point behind doing theoretical research. As a PhD student one must show that one has learnt if not mastered the art of working with fresh theoretical concepts in a logical, consistent, manner. I did show some ability in this regard, and this part of the work does not get much affected by a re-evaluation of the theory in the light of the fresh experimental evidence.

Fourthly, though now there remains little to my theory if it is taken as an integrated whole, the fact of the matter is, in the process of having worked hard to build a model that later on turns out to be erroneous, I learnt a lot even before the error could be detected. And, thus, presenting a better model would be far easier. Indeed to the experts I can already tell on the fly: For a universe consisting only of electrons as fermions and photons as bosons, a model whereby the fermion is the pollen-grain and the photons are the bumping particles can easily be built, after throwing in a set of rules to get the phases (including spin and chirality) right. [Update on 2014.12.28: And, of course, while writing this post itself, I did know that a clarification for the creation and annihilation operators would be necessary, too. I just forgot to mention it in the original post.] No, I am not going to rush building one immediately. I just wanted to point out how easy it becomes to build a new, consistent, theory. The required integrations are already there.

That’s why, even if I guess I will have to withdraw the theory, I call it as being only partly wrong.

[Update on 2014.12.28: I think I should still pursue obtaining precise experimental evidence, before formally withdrawing my theory.]

A few other notes:

I didn’t know about the PDC photons or their behavior when I built my theory. No researcher/reviewer pointed it out to me, perhaps because they didn’t make the connection themselves. Realize, in the absence of the knowledge of the ballistic dynamics of the PDC photons, mine is a perfectly sensible theory. The very words ballistic vs. diffusive is something I read for the first time while casually browsing the home page of the optics group at the Raman Research Institute last year or so. I still don’t know whether the terms technically apply the issue I outlined above, but still, presumably, I have made clear the error I made.

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Now, on to the part where I am fully right. This, of course, concerns the diffusion equation.

The experiment that any one could perform at home (the one I hinted at, in my last post) consists of this one:

Take a blotting paper and put a small drop of blue ink in the centre. Watch the boundary separating the blue and white portions grow. [Yes, I know I have mentioned this experiment in my blog posts before. But now there is a bit of a new angle, so read on anyway.]

The Fourier theory does not acknowledge the existence of this front. In Fourier theory, the blueness is spread over the entire paper right from the word go.

If possible, make a video of the front, and find out the speed of the propagation of the front.

By arguments rooted in the numerical analysis methods, as well as by Einstein’s stochastic approach, the theory predicts a uniform speed of propagation for the front. (In Einstein’s theory, it’s stochastically uniform.) In Fourier’s theory, the concept is inapplicable and hence, if it at all must be used, then it can be said that the front has an infinite speed. [Since the blotting paper experiment does not fulfil all the requirements of the diffusion equation, your experimentally observed front may not have a uniform outward speed. But, the experiment does fulfil the aspect of a support limited to a sub-domain vs. that over the full domain.] [Update on 2014.12.28: Drop me a line if you want to perform a more complicated experiment that should conform to the diffusion equation better, at home or at school/college lab, and I will give you a few ideas.]

Here is another funny thing. Suppose the initial concentration/temperature profile is in the form of the cosine curve in between $-\pi$ to $+\pi$, and that the domain also runs between the same limits. If you know Fourier’s theory, you know that essentially, we are simplifying the situation to the greatest extent by taking just a single basis function in the Fourier expansion (i.e., apart from the bias, which, for diffusion of mass, would have to be taken as $-1$ here).

Suppose further that the boundary conditions are maintained to be zero field variable (concentration/temperature) at both the endpoints.

Since the profile covers the entirety of the domain, the solution at every point, throughout the diffusion, would consist of only a cosine curve; it’s just that its height would go on dropping with exponential decay, as the diffusing species goes out of the domain.

Now, do a funny thing. Keep the initial profile as in the above example, but let the domain run from $-10 \pi$ to $+10 \pi$.  The boundary conditions continue to remain the same: zero field variable.

If your intuition is like mine, we would expect the solution in the two cases to remain the same. But, in Fourier’s theory, they are not.

Since the domain size has increased, there is a portion $9 \pi$ long on each side of the initial profile that must be brought into the initial Fourier expansion. This introduces an infinity of basis functions into the initial profile. Naturally, the profile at any future time also is different from the first case.

[Update on 2014.12.28: I had also thought of mentioning the fact that the Fourier solution would be still different for a domain of total size $\pm 2 \pi$, but forgot to write about it in the original post.]

To a mathematician (and to any modern theoretical physicist—the same ones who can’t detect a mistake in my QM papers), the existence of different solutions for the same set of initial and boundary conditions, makes perfect sense. At least they don’t seem to notice anything amiss here. But what their position implies is the following, for your experiment at home.

If you take a bigger blotting paper, the shape of the solution should be different.

In other words, in Fourier theory, the solution crucially depends on the domain size, too—not just on the local dynamics of the diffusing species.

The experiment which I was going to request, would have made use of this domain-size dependence, for photons propagation. But then, as I said, I caught my own error, and so, I am not going to request performance of that kind of an experiment.

But what about the intuition, you say?

Well, if you take a local theory—Einstein’s stochastic, or those having roots in the numerical methods (and I need to give a name to these, just for convenience in reference)—the solution profile remains identical regardless of the domain size.

[Update on 2014.12.28: Indeed, you could even cut a significant portion of the paper near one of its edges after the diffusion has already begun, so long as the blue front has not reached that place, and it would still not affect the solution. I forgot to mention this point while writing the original version of this post.]

Getting more technical once again: There also is an implication for the instantaneous flux rate and the total outward flux, for the two theories. The local theories predict a zero flux until the front reaches the boundary. But since the diffusing species is conserved (conservation of mass or heat power, etc.), what it implies is that the local theories must give a faster flux rate at the times after the front reaches the boundary.

Keeping the conservation angle aside, the zero-flux state is something that should be easily verifiable in experiment. If it is experimentally verified, then, the local-physics theories win; else, the Fourier theory does.

I bet that the local theories would win. There is no blueness near the edges until the front travels there.

And, as far as I can tell, even if not photons, at least electrons do obey the diffusive dynamics in the free space. If careful experimentation is conducted, I predict (even ahead of building my new quantum theory) that there should be an experimentally verifiable zero-flux period, in contradiction to the mainstream quantum mechanics. And if it is observed, then it means that many mainstream ideas—or their mystifying components, at least—are completely wrong.

For this very reason, I don’t expect them to conduct the necessary experimentation with electrons. Or, try to think of any novel experimentation scheme with PDC photons.

In the meanwhile, I will build my new theory. However, now with another difference. The last time, I was content identifying the photon as a local condition, without specifying anything regarding its structure or the local dynamics. That was because, as a PhD student in engineering, I couldn’t afford to be too speculative. Now, however, I can afford to be a bit more relaxed, and begin considering toy ideas for more detailed models for the quanta. Inasmuch as photons are massless and there is aether, the situation is ripe for me to toy with some fluids-based ideas or models. Since I anyway do CFD, no one in engineering would even notice what I was doing was toying with some QM-related ideas. … Nice, no?

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Anyway, best wishes for a merry Christmas, and a very happy and prosperous new year. … No, I don’t think I will be writing any post in the remaining parts of this year. So, there. Wish you a very happy and prosperous new year, too…

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A Song I Like:

(Hindi) “jalate hain jis ke liye…”
Singer: Talat Mahmood
Music: S. D. Burman
Lyrics: Majrooh Sultanpuri

[As usual, I may come back and do some minor copy-editing and additions, though the main matter will remain as is. [Update on 2014.12.28: Done. I won’t bother any more with this post. If anything more is to be added, I will simply write a fresh post.]]

[E&OE]

# An Important Comment I Just Made at iMechanica—And, (Much) More!

0. The title says it all!

Go, check out this comment I just made at iMechanica: [^].

1. Now, on to the “more” part of the title. Noted below are a few more things about my research.

2. My Researches on QM:

2.1 Since the publication of my QM-related results, I have moved on considerably further. As mentioned earlier on this blog, I have since then realized that my approach—the way I thought about it, as in contrast to what I (happened to have) published—always could handle the vector field equations of electromagnetism, including those for light. That is, including the angular momentum part of the EM fields. (Paddy, Suku, are you listening?) … However, I decided against publishing something in more detail to cover this aspect. A good decision, now it seems in retrospect.

(Yes, Jayant, you may now try your best to prod me towards publishing, including emphasizing how unpublished research is non-existent research. Just try it! Any which way you wish. … Precisely just the way I don’t give a damn to wannabe physicists turning JPBTIs turning entrepreneurs, I also don’t give a damn to the Statism-entrenching advices coming off the Statism-entrenching scientists, esp so if they also are the State-revered ones. So, just try it!! Also others, like, say, Sunil!!!)

2.2 I had also resolved the entanglement issue, and have chosen not to publish about it. As I stated earlier here [^], Louisa Guilder reports that Bell’s inequality paper has garnered the highest number of citations in physics literature so far, an astounding 2,500. The paper # 2,501 (or greater, as of today) must have concluded that the entanglement issue cannot be resolved—possibly out of the position/conviction that there was nothing to be resolved.

So, basically, I have resolved what an enormous number of misguided (and, possibly outright stupid) people could cite but not resolve.

Aside: Of the hundreds of papers on this topic I have come across, I know of Dr. Joy Christian’s position to be most reasonable—and in my knowledge, only his. Now, there are some minor differences between what he says and what I have always known and never published. But these differences are, in a sense, minor. The important part—and aren’t we concerned only with the important things here?—is that I knew about it, and have deliberately chosen not to publish about it. (If holding this position makes it possible to tick me off via certain lists such those maintained by a John Baez or a Scott Aaronson, I couldn’t care less about it—and both (and all) of them, I suppose, should know/could get to know, how (I care so less about those lists).)

BTW, as a matter of progression in time, I had thought that the issue would have to be first resolved in the context of photons, not of electrons. I am not very sure about it, though. In any case, that was the sequence in which I did it. First, photons; then, electrons.

Go, try your best to prod me towards publishing something on it! Just try it!! … BTW, my resolution had happened years before I had publicly offered an Indian PhD physicist on a “LinkedIn” group that I could explain my results if she (or anyone else) could meet me in person at Pune. This public offer of mine has just ended, right now!…. So, go ahead! Just try it!!!

3. My Researches on Other Topics

3.1 I have had some definite ideas for research on other topics from computational science and engineering and allied fields (including a numerics). I have kept these aside for the time being, because many of these are well-suited for guiding PhDs. Which brings me to the last couple of points for today (or at least, as of now, in the first version of this post).

3.2 As to student projects, I have decided not to accept anyone unless he is remarkably bright, and hard-working. (For those who seek to do truly independent PhD research, I cannot make myself available as a guide, as of now. Also see the point 3.3 below.) Roughly speaking, this means that rough level as would be understood by one or more of the following: GRE (V+Q) scores of at least 1350; GATE score of 95+P; throughout distinction class (or in at least 5 semesters out of 8) in BE of University of Pune (or equivalent).

3.3 The University of Pune has a stupid requirement for becoming a PhD guide: you (i.e. a fresh PhD graduate) must wait for at least 3 years after his own (successful) defense before he can become a PhD guide himself. The three years, in my case, end on September 20, 2012. (They—the Indian government(s)—probably arranged the date to numerically coincide with the date on which I first entered USA: 2nd September, 1990. Yes, the same government that whispered the UK government to give Rahul Gandhi’s brother-in-law all security clearance at UK airports, on par with the President and Prime Minister of India.)

Recently, someone reminded me a further requirement that I had forgotten. You also need to have two publications in those three years, before you can become a guide. Since I have mentioned the Gandhi’s and the defence-date here, I am sure that they would now interpret the sufficiently vague rules to imply that those two must be journal articles—peer-reviewed conference proceedings won’t do.

I, therefore, have decided to try to publish two journal articles in the near future of a few months. (Hey Elsevier, take notice!)

At least one, and probably both of these two articles would be on CFD.

Those of you who know me, would know that once I get going, I get going. I don’t disappoint (these of) you, not this time around at least: I have already installed Ubuntu 11.10 (natty) inside Oracle’s VirtualBox running on top of Windows (32 bit XP and 64-bit 7), and have already installed OpenFOAM v. 2.0.1 in that Ubuntu (32-bit, as of now). I also have installed other software. I have shortlisted the niche problems I could work on. I have contacted a couple of IIT Bombay professors, not for collaboration, but merely for sounding out. I knew that being employed by the IIT Bombay, there would be no collaboration, though a collaboration could have been perfectly OK by me. I also knew that once I wrote an email to them, it would get trapped (as all my emails are), and then, even the sounding things out over a 30 minute session would soon become impossible. And, that the impossibility would never be communicated explicitly via any means, esp. via an email. This  supposition of mine has indeed come to pass. (Congratulate me for being a good judge of the IIT Bombay, of the Indian government(s)—all of them, today’s and those of the past under the BJP regime as well, of Indians, and of humanity in general.) I knew all that, right in advance, and had prepared myself mentally for it. And, thought of plans B and C as well. I am executing on these.

And, no, I couldn’t care a hoot for how many freaking citations those two journal papers generate. As far as I am concerned, these two papers would allow me to fulfill the stupid requirements whereby I can become a PhD guide. And whereby, a slim chance does exist that I might get some good guy (gals included) for PhD supervision. (Chances are, it could be someone I already knew as a friend—numerically speaking, most of my friends are without PhDs.)

So, there. For the next few months, that’s the sort of research I am going to do—in my spare time, of course. Hey Elsevier, take notice (once again!!). As to others: If you consider yourself my friend, help me publish it in an easy and timely manner, ASAP.

That’s all for today. For this first version, anyway. As always, I might come back and correct or add a few things. …. Might as well add a few political comments right here.

4. A Few Comments on Politics and All:

Just noting down a few comments on politics (i.e. that politics which is “larger” than the one in S&T fields) in passing (and I will take liberties to pass comments on people without alerting them):

To ObjectivistMantra and Others:

I think I will stop here, and add possibly add other points via other blog posts. For the time being, as far as politics goes, I am enjoying (“loving it”) watching the BJP more than anyone else in the opposition/government, as far as the issue of retail FDI goes.  However, I am not going to support Walmart for the simple reasons that (i) their country has unreasonably failed me in the PhD and unreasonably denied me green-card/citizenship, (ii) they are too big to need my support anyway, and (iii) supporting a big company against government—Microsoft, in the DoJ case—was one among many things that got me a heart condition, I know. (How do I know? Well, it’s the same guy who has known how to resolve the QM wave-particle duality in the context of light, and about angular momentum in EM, and then, a resolution of the riddles of quantum entanglement, as well as many other unpublished, even un-discussed topics.)

One final point, again going back towards research. For the past several years I could not fathom the reason why people might be so unenthusiastic about my approach—I mean, honest people (apart from all the dirty things and “political” issues I have mentioned/indicated above.) Well, it was while reading Sean Carroll’s blog at Discovery magazine that I happened to realize one important (technical) reason why this might be (or must be) so! Hmmm…. Nice to know. It’s always great to know. Though, I am not going to divulge here what that thing was—or how it not only doesn’t contradict my approach but rather helps me be even more confident about my approach (if I ever needed such help, in this context!) And, as you know, I am not going to discuss it or publish about it either. Try to get me to do otherwise. … Just try!
Ok. Enough is enough. As usual, to be edited/streamlined later—perhaps!

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A Song I Like:
[RIP, Dev Anand!]
(Hindi) “gaataa rahe, meraa dil…”
Music: S. D. Burman (perhaps with R.D. looking after the orchestra (??) if not also the tune. (I have read somewhere that he was involved in “Aaraadhanaa,” but have no such idea when it comes to “Guide”)
Singers: Kishore Kumar, Lata Mangeshkar
Lyrics: Shailendra

[E&OE]